Matrix3d m;
m << 1, 1, 0, 1, 3, 2, 0, 1, 1;
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Notice that the middle column is the sum of the two others, so the "
	 << "columns are linearly dependent." << endl;
cout << "Here is a matrix whose columns have the same span but are linearly independent:" << endl
	 << m.fullPivLu().image(m) << endl;
